Shannon Defines a model as- A Representation of an object, a system, or an idea in some form other than that of the entity itself.

1. Introduction to Simulation
modeling
Submitted To:-
Prof. D.K. Chaturvedi,
Electrical Department,
Faculty of Engineering,
Dayalbagh Educational Institute,
Dayalbagh, Agra.
Submitted By:-
Bhupendra Kumar
M.Tech(Int.) – 094008

2. Introduction to model
Shannon Defines a model as-
A Representation of an object, a system, or
an idea in some form other than that of the
entity itself.

3. Definition - Simulation
“Simulation is the process of designing
a model of a real system and conducting
experiments with this model for the
purpose of either understanding the
behavior of the system and/or
evaluating various strategies for the
operation of the system.”
- Introduction to Simulation Using SIMAN
(2nd Edition)

4. Some other definitions
• The technique of imitating the behavior of
some situation or system by means of an
analogous model, situation, or apparatus,
either to gain information more conveniently
or to train personnel.
• Simulation:
– “… as a strategy – not a technology – to mirror,
anticipate, or amplify real situations with guided
experiences in a fully interactive way.”

5. Simulation
• Where simulation fits in
Simulation
Programming
Analysis
Modeling
Probability &
Statistics

6. 6
• Ways to study a system
Systems, Models, and Simulation

7. 7
Elements of Simulation Analysis
Problem Formulation
Data Collection and Analysis
Model development
Model Verification and Validation
Model Experimentation and Optimization
Implementation of Simulation Results
Major Iterative Loops in a Simulation Study

8. Brief history
• World War II
• “Monte Carlo” simulation: originated with the work on
the atomic bomb. Used to simulate bombing raids. Given
the security code name “Monte-Carlo”.
• Late ‘50s, early ‘60s
• First languages introduced: SIMSCRIPT, GPSS (IBM)
• Late ‘60s, early ‘70s
• GASP IV introduced by Pritsker. Triggered a wave of
diverse applications. Significant in the evolution of
simulation.

9. • Late ‘70s, early ’80
• SLAM introduced in 1979 by Pritsker and Pegden.
• Models more credible because of sophisticated tools
• SIMAN introduced in 1982 by Pegden. First language to
run on both a mainframe as well as a microcomputer.
• Late ‘80s through present
• Powerful PCs
• Languages are very sophisticated (market almost saturated)
• Major advancement: graphics. Models can now be
animated!

10. Simulation modeling perspectives
• Can be used to study simple systems
• Good for comparing alternative designs
– More complex techniques allow “optimization” using a
simulation model
• can be used to understand the behavior of the system or evaluate
strategies for the operation of the system
• Model complex systems in a detailed way
• Construct theories or hypotheses that account for the observed
behavior
• Use the model to predict future behavior, that is, the effects that
will be produced by changes in the system
• Analyze proposed systems

11. 11
SIMULATION “WORLD-VIEWS”
Pure Continuous Simulation
Pure Discrete Simulation
– Event-oriented
– Activity-oriented
– Process-oriented
Combined Discrete / Continuous Simulation

12. 12
Examples Of Both Type Models
Continuous Time and Discrete Time
Models:
CPU scheduling model vs. number of
students attending the class.

13. Advantages to Simulation:
• Can be used to study existing systems without disrupting the
ongoing operations.
• Proposed systems can be “tested” before committing resources.
• Allows us to control time.
• Allows us to identify bottlenecks.
• Allows us to gain insight into which variables are most
important to system performance.
• Flexibility to model things as they are (even if messy and complicated)
Allows uncertainty, nonstationarity in modeling

14. Some Primary Uses of Simulation
Models in Operations
• Find the bottlenecks
• How are resources utilized
• Capacity planning
• Impact of configuration changes
• Understand the system dynamics

15. Disadvantages to Simulation
• Model building is an art as well as a science. The quality
of the analysis depends on the quality of the model and the
skill of the modeler.
• Simulation results are sometimes hard to interpret.
• Simulation analysis can be time consuming and expensive.
Should not be used when an analytical method would
provide for quicker results.
• Not guarantee to provide optimal solution

16. Limitations & pitfalls
• Failure to identify objectives clearly up front
• In appropriate level of detail (both ways)
• Inadequate design and analysis of simulation
• experiments
• Inadequate education, training
• Failure to account correctly for sources of
randomness in the system under consideration
• Failure to collect good system data, e.g. not enough
data to create a good model

17. 17
Applications:
Designing and analyzing manufacturing
systems
Evaluating H/W and S/W requirements for a
computer system
Evaluating a new military weapons system or
tactics
Determining ordering policies for an
inventory system
Designing communications systems and
message protocols for them

18. 18
Applications:(continued)
Designing and operating transportation
facilities such as freeways, airports, subways,
or ports
Evaluating designs for service organizations
such as hospitals, post offices, or fast-food
restaurants
Analyzing financial or economic systems
material handling systems, assembly lines,
automated production facilities.

19. Hand and manual simulation concepts
• The numerical methods for manual simulation
can be classified into the following two
classes:
• 1. One-step or single-step method
Euler’s method, Runge–Kutta method.
• 2. Multistep method
Milne, Adams–Bashforth methods, predictor
corrector method.

20. One-Step vs Multi-Step

21. 21
Euler Method
• Modified Euler method is derived by applying the trapezoidal
rule to integrating ; So, we have
• If f is linear in y, we can solved for similar as backward
Euler method
• If f is nonlinear in y, we necessary to used the method for
solving nonlinear equations i.e. successive substitution
method (fixed point)
),(' tyfyn 
),('),(
2
''
11 nnnnnnn tyfyyy
h
yy  
1ny

22. 22
Example: solve
Solution:
f is linear in y. So, solving the problem using modified Euler
method for yields
25.0,10,1)0(,1' 0  htyytyy
hy
t
h
t
h
y
ht
h
yt
h
y
ytyt
h
y
yy
h
yy
n
n
n
n
nnnn
nnnnn
nnnn












1
1
11
111
11
)
2
1(
)
2
1(
)
2
1()
2
1(
)11(
2
)''(
2
ny

23. 23
Graphthe solution

24. Predictor-Corrector Methods
• The Predictor-Corrector technique uses an explicit
scheme (like the Adams-Bashforth Method) to
estimate the initial guess for xi+1 and then uses an
implicit technique (like the Adams-Moulton Method)
to correct xi+1.

25. Predictor-Corrector Example
• Adams third order Predictor-Corrector scheme:
• Use the Adams-Bashforth three point explicit scheme
for the initial value.
• Use the Adams-Moulton three-point implicit method
to correct.
 2i1iii1i 51623
12
*   fff
h
xx
 ),(),(8),(5
12
11
*
11i1i   iiiiii xtfxtfxtf
h
xx

26. Predictor-Corrector Example
• Consider Exact Solution
• Initial condition: x(0) = 1
• Step size: h = 0.1
• We will use the 3 Point Adams-Bashforth and 3 point
Adams-Moulton. Both require 3 points to get
started!
2
tx
dt
dx
 t2
22 ettx 

27. Predictor-Corrector Example
• From the 4th order Runge Kutta
• 3-point Adams-Bashforth Predictor Value:
 
340184.1121587.0218597.1
)1(5)094829.1(16)178597.1(23
12
1.0
2
*
3

 xx
 
 
 
218597.1
178597.1218597.1,2.0
094829.1104829.1,1.0
0000.11,0
2
2.0
1.0
0




x
ff
ff
ff

28. Predictor-Corrector Example
• To correct, we need f(t3 , x3
*)
• 3-point Adams-Moulton Corrector Value:
  250184.1340184.1,3.0 f
      
340138.1
121541.0218597.1
094829.11178597.18250184.15
12
1.0
23


 xx

29. The values for the Predictor-Corrector Scheme
Three Point Predictor-Corrector Scheme
t x f A-B sum x* f* A-M sum
0 1 1
0.1 1.104829 1.094829
0.2 1.218597 1.178597 0.121587 1.340184 1.250184 0.121541
0.3 1.340138 1.250138 0.128081 1.468219 1.308219 0.12803
0.4 1.468168 1.308168 0.133155 1.601323 1.351323 0.133098
0.5 1.601266 1.351266 0.136659 1.737925 1.377925 0.136597
0.6 1.737863 1.377863 0.138429 1.876291 1.386291 0.138359
0.7 1.876222 1.386222 0.13828 2.014502 1.374502 0.138204
0.8 2.014425 1.374425 0.136013 2.150438 1.340438 0.135928
0.9 2.150353 1.340353 0.131404 2.281757 1.281757 0.13131
1 2.281663 1.281663 0.124206 2.405869 1.195869 0.124102
Predictor-Corrector Example

30. The predictor-corrector method
produces a solution with nearly the
same accuracy as the RK order 4
method.
Generally, the n-step method will
have truncation error of order at
least n.
-10
-8
-6
-4
-2
0
2
4
0 1 2 3 4
xValue
t Value
3 Point Predictor-Corrector Method
4th order Runge-Kutta
Exact
Adam Moulton
Adam Bashforth
Predictor-Corrector Example